Q. 23 - Calculus

Question

Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises $21-28$.

${\int }_{-3}^{8}24dx$.

Step-by-Step Solution

Answer

The exact value of ${\int }_{-3}^{8}24dx$ is, $264$.

Step 1 . Given information

${\int }_{-3}^{8}24dx$.

Step 2 . The following figure shows the graph of y = 24 .

Step 3 . Find the area.

The area of the shaded rectangle is,

$$\begin{gathered} l\times b=11\times 24 \\ =264 \end{gathered}$$

Therefore, the exact value is, $264$.